The Assembly easily approved the bill, but the Republican-led state Senate is one vote shy of passage. Supporters say the momentum is on their side.

Reporting from New York — New York, where the gay rights movement was born but has run up against conservative forces, could again change the political landscape for gays by becoming the largest state to allow same-sex marriage.

Advocates guided by first-term Democratic Gov. Andrew Cuomo have been maneuvering before the end of the legislative session Monday to get the one vote needed to win approval in the Republican-led state Senate. Supporters say the momentum is on their side, but opponents are still pushing to prevent the measure from reaching the Senate floor.

Although five states allow gay couples to marry, New York would be by far the most populous and diverse state to do so. Opponents point to voter defeats of same-sex marriage laws in 31 other states, but nationwide polls show growing acceptance of the idea. A wave of gay and lesbian marriages in New York would establish a new reality that defenders of traditional marriage might find difficult to overcome in public opinion or the courts.

California voters approved Proposition 8 to ban same-sex marriage after it was briefly legal in 2008. A federal judge later declared Proposition 8 unconstitutional; his ruling is on hold pending appeal.

On Wednesday, the Democratic-dominated Assembly easily approved the bill a fourth time, but the Senate remained divided, with 31 of 62 senators committed to approving it. Senate Republicans spent most of Thursday behind closed doors debating the issue, as well as important local bills.

For months, a parade of glitterati have lined up to voice their support for same-sex marriage — including movie stars, athletes and Wall Street titans, as well as New York's billionaire Mayor Michael R. Bloomberg, who flew to Albany on Thursday to appeal again to GOP senators.

But while stars of "Sex and the City" and beefy hockey players are a media draw, the focus is on a handful of little-known Republican lawmakers from Westchester County, Long Island and Poughkeepsie, where GOP voters tend to be moderates.

In New York, advocates have come together to mount a highly orchestrated, energetic and expensive campaign to persuade legislators to support the issue. The election of Cuomo last year, who made this issue a priority, gave the movement momentum. He is said to be spending a lot of time on the phone and meeting with fence-sitting lawmakers — talking about public support for the issue and offering political protection to nervous legislators.

Proponents have spent at least $2 million on advertising, on 250,000 pieces of direct mailing, on phone banks and organizing volunteers to walk the streets of districts of key wavering senators from both parties. And for the first time in New York history, Republicans donated to the effort that has traditionally been dominated by Democrats. Opponents have been less visible, running a few television ads.

New York has long been more liberal than the rest of the country, but also has a strong streak of social conservatism, particularly on issues that involve the Catholic Church and Latinos.

New York Archbishop Timothy Dolan has been a central opponent of the same-sex marriage bill, and has written regularly on his blog of the perils of defining marriage as anything other than between a man and a woman in a "loving, permanent, life-giving union to procreate children."

"Yes, I admit, I come at this as a believer, who, along with other citizens of a diversity of creeds believe that God, not Albany, has settled the definition of marriage a long time ago," he wrote Tuesday.

To assuage religious leaders, the measure introduced by Cuomo on Tuesday would excuse their institutions from any obligation to solemnize or provide facilities for same-sex weddings.

That didn't satisfy New York's formidable Conservative Party, which has made it clear that any GOP senator who votes for the marriage bill will lose its crucial support.

"Any Republican who votes for this will not be on the conservative line," said Conservative Party Executive Director Shaun Marie. "They don't carry conservative values and there's no sense in telling people that they do."

Two Republicans, James S. Alesi of Monroe County and Roy J. McDonald of the area around Albany, have said they would join 29 of 30 Senate Democrats in backing the bill. One Democratic senator, a Pentecostal minister from the Bronx, has long said he would not condone gay marriage.

Public opinion polls in New York and nationwide have found that 55% to 58% of the population is at ease with same-sex couples being allowed to marry — and support is considerably higher among younger people.